Table 1: Environmental Means

EnviroMean <- 
  results %>% 
    select("Day", "Temperature", "pH", "Temp","pHspec", "pCO2out", "AlkTotal") %>%
    filter(Day >= "1", Day <= "123") %>%
    drop_na(Day) %>% 
    group_by(Temperature, pH) %>% 
    summarise(mean_T = mean(Temp, na.rm = T),
              se_T = sd(Temp, na.rm = T)/sqrt(6),
              min_T = min(Temp, na.rm = T), 
              max_T = max(Temp, na.rm = T),
              mean_pH = mean(pHspec, na.rm = T), 
              se_pH = sd(pHspec, na.rm = T)/sqrt(6),
              mean_pCO2 = mean(pCO2out, na.rm = T), 
              se_pCO2 = sd(pCO2out, na.rm = T)/sqrt(6),
              mean_AlkTotal = mean(AlkTotal, na.rm = T),
              se_AlkTotal = sd(AlkTotal, na.rm = T)/sqrt(6))

EnviroMean %>% 
  kbl(caption = "Table 1: Experimental treatments and environmental conditions (mean +/- standard error) of the 126-day experiment.") %>% 
  kable_classic_2() %>% 
  kable_styling(c("striped", "hover"), full_width = F, html_font= "Times New Roman")

Table 1: Experimental treatments and environmental conditions (mean +/- standard error) of the 126-day experiment.

Temperature	pH	mean_T	se_T	min_T	max_T	mean_pH	se_pH	mean_pCO2	se_pCO2	mean_AlkTotal	se_AlkTotal
ambient	acidified	24.79000	0.8869310	22.07	27.36	7.644120	0.0101512	1082.9250	65.31879	2142.000	112.494347
ambient	ambient	24.78429	0.8856820	22.09	27.40	7.961042	0.0146725	480.8325	22.56737	2181.872	5.679540
heated	acidified	26.73429	0.8269073	23.75	29.38	7.662486	0.0129196	1106.5750	77.15382	2137.082	123.057409
heated	ambient	26.70434	0.8184090	23.82	29.34	7.956690	0.0141496	524.3757	20.91815	2180.797	5.838938

Environmental <- 
  results %>% 
    select("Day", "Temp", "pH", "Temperature","pHspec","Header", "TankID") %>%
    filter(Day >= "1", Day != "126") #use only days from start of experiment when desired conditions were reached
  

#temp between high and ambient temp
tempmod<-aov(Temp ~ Temperature, data=Environmental)
summary(tempmod) #temperature was different between high and ambient treatment

#pH between high and ambient co2
summary(aov(pHspec ~ pH, data=Environmental)) #pH was different between high and ambient co2 treatments



##HEADERS
#temp between headers in high
aov1<- Environmental %>%
  filter(Temperature=="heated")

modaov1<-aov(Temp ~ as.factor(Header), data=aov1)

summary(modaov1) #not different between headers

#temp between headers in ambient temp
aov2<- Environmental %>%
  filter(Temperature=="ambient")

summary(aov(Temp ~ as.factor(Header), data=aov2)) #not different between headers

#pH between headers in acidified
aov3<- Environmental %>%
  filter(pH=="acidified")

summary(aov(pHspec ~ as.factor(Header), data=aov3)) #not different between headers

#pH between headers in ambient pH
aov4<- Environmental %>%
  filter(pH=="ambient")

summary(aov(pHspec ~ as.factor(Header), data=aov4)) #not different between headers


##TANKS
#temp between tanks in high temp
aov1<- Environmental %>%
  filter(Temperature=="heated")

summary(aov(Temp ~ as.factor(TankID), data=aov1)) #not different between heated tanks

#temp between tanks in ambient temp
aov2<- Environmental %>%
  filter(Temperature=="ambient")

summary(aov(Temp ~ as.factor(TankID), data=aov2)) #not different between ambient tanks

#pH between tanks in acidified
aov3<- Environmental %>%
  filter(pH=="acidified")

summary(aov(pHspec ~ as.factor(TankID), data=aov3)) #not different between tanks in acidified

#pH between headers in ambient pH
aov4<- Environmental %>%
  filter(pH=="ambient")

summary(aov(pHspec ~ as.factor(TankID), data=aov4)) #not different between headers

Table 2: Results of ANOVA for environmental

Treatment Comparison	Pr(>F)
Heated v. Ambient	<0.001
Acidified v. Ambient	<0.001
Ambient temp headers	0.998
Heated headers	0.842
Ambient pH headers	0.129
Acidified headers	0.150
Ambient temp tanks	1.000
Heated tanks	0.999
Ambient pH tanks	0.675
Acidified tanks	0.888

Check assumptions of treatment conditions model

#check assumptions
# 1. Normality of residuals
qqPlot(residuals(tempmod)) #very much not normal

shapiro.test(residuals(tempmod)) # nope
hist(residuals(tempmod)) #nope...

#check assumptions
# 2. Equal variances
#leveneTest(residuals()~$)
#plot(fitted(),resid(,type="pearson"),col="blue")

Check using nonparametric Kruskal-Wallis test

# did i set this up right?
kruskal.test(Environmental$Temp~Environmental$Temperature)# **diff

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Environmental$Temp by Environmental$Temperature
## Kruskal-Wallis chi-squared = 203.29, df = 1, p-value < 2.2e-16

kruskal.test(Environmental$pHspec~Environmental$pH)# **diff

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Environmental$pHspec by Environmental$pH
## Kruskal-Wallis chi-squared = 470.87, df = 1, p-value < 2.2e-16

kruskal.test(Environmental$pHspec~Environmental$Temperature)# Not dif

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Environmental$pHspec by Environmental$Temperature
## Kruskal-Wallis chi-squared = 0.080493, df = 1, p-value = 0.7766

kruskal.test(Environmental$Temp~Environmental$pH)# not dif

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Environmental$Temp by Environmental$pH
## Kruskal-Wallis chi-squared = 0.18832, df = 1, p-value = 0.6643

i. Day -24

Assemble data for diameters of initial collection of urchins from hatchery and calculate mean

##Initial Collection = Day -24
InitialDiameter <-
  #seperate out the initial sizes of urchins on day -24 after initial collection.
  results %>% 
    select("Day", "Diam1", "Diam2", "TankID", "Temperature", "pH", "Treatment") %>%
    filter(TankID != "8t" ) %>% 
      #remove urchin number 8 which died halfway through
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column in order to make number of levels of each grouping factor < number of observations (as per error message previously recieved)
    filter(Day == "-24") %>% 
      #sizes on day -24  
    select("TankID", "Diameter", "Temperature", "pH", "Treatment")


InitialMean <- mean(InitialDiameter$Diameter)
InitialSE <- sd(InitialDiameter$Diameter)/sqrt(23)

InitialMean
InitialSE

ii. Day -13

Assemble Data for diameters of acclimated urchins before conditioning and calculate mean

##After acclimating before ramp up = Day-13

AcclimatedDiameter <-
  #seperate out the initial sizes of urchins on day -24, when desired conditions were met.
  results %>% 
    select("Day", "Diam1", "Diam2", "TankID", "Temperature", "pH", "Treatment") %>%
    filter(TankID != "8t" ) %>% 
      #remove urchin number 8 which died halfway through
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column in order to make number of levels of each grouping factor < number of observations (as per error message previously recieved)
    filter(Day == "-13") %>% 
      #sizes on day -24  
    select("TankID", "Diameter", "Temperature", "pH", "Treatment")


AcclimatedMean <- mean(AcclimatedDiameter$Diameter)
AcclimatedSE <- sd(AcclimatedDiameter$Diameter)/sqrt(23) 

AcclimatedMean
AcclimatedSE

iii. Day 1

Assemble Data for diameters on day 1 of experiment when desired conditions were reached

##After ramp up and desired conditions are reached to begin experiment = Day 1

Day1Diameter <-
  #seperate out the initial sizes of urchins on day 1, when desired conditions were met.
  results %>% 
    select("Day", "Diam1", "Diam2", "TankID", "Temperature", "pH", "Treatment") %>%
    filter(TankID != "8t" ) %>% 
      #remove urchin number 8 which died halfway through
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column in order to make number of levels of each grouping factor < number of observations (as per error message previously recieved)
    filter(Day == "1") %>% 
      #sizes on day 1  
    select("TankID", "Diameter", "Temperature", "pH", "Treatment")


Day1Mean <- mean(Day1Diameter$Diameter)
Day1SE <- sd(Day1Diameter$Diameter)/sqrt(23)

Day1Mean
Day1SE

iv. Day 126

Assemble Data for diameters on day 126 of experiment after full growth

##After ramp up and desired conditions are reached to begin experiment = Day 1

Day126Diameter <-
  #seperate out the initial sizes of urchins on day 1, when desired conditions were met.
  results %>% 
    select("Day", "Diam1", "Diam2", "TankID", "Temperature", "pH", "Treatment") %>%
    filter(TankID != "8t" ) %>% 
      #remove urchin number 8 which died halfway through
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column in order to make number of levels of each grouping factor < number of observations (as per error message previously recieved)
    filter(Day == "126") %>% 
      #sizes on day 1  
    select("TankID", "Diameter", "Temperature", "pH", "Treatment")


Day126Mean <- mean(Day126Diameter$Diameter)
Day126SE <- sd(Day126Diameter$Diameter)/sqrt(23)

Day126Mean
Day126SE

i. Growth Analysis

Assemble data and calculate means using day 1 as initial diameter and calculate means

### GROWTH MODEL 1: using day 1 as the first official day of experiment when desired environmental conditions were met (24 days after getting urchins. In that 24 days, they were acclimated and then conditions ramped up)

Initial <-
  #seperate out the initial sizes of urchins on day 1, when desired conditions were met to standardize growth to this measurement.
  results %>% 
    select("Day", "Treatment", "Temperature", "pH", "Diam1", "Diam2", "TankID") %>%
    filter(TankID != "8t" ) %>% 
      #remove urchin number 8 which died halfway through
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column in order to make number of levels of each grouping factor < number of observations (as per error message previously recieved)
    filter(Day == "1") %>% 
      #sizes on day 1  
    select("Temperature", "pH", "Diameter", "TankID")

  
Final <- 
  #seperate out the final sizes of urchins on day 126
   results %>% 
    select("Day", "Treatment", "Temperature", "pH", "Diam1", "Diam2", "TankID") %>% 
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
      #gather Diam1 and Diam2 into single column
    filter(Day == "126") %>% 
      #filter for sizes on day 126
    select("Temperature", "pH", "Diameter","TankID")


Growth <- 
  #create column that is growth
  bind_cols(Initial, Final) %>% 
    #binds initial (Diameter) and final (Diameter1) sizes to calculate growth
  mutate(Growth = ((Diameter1 - Diameter)/Diameter*100)) %>% 
    #add column for growth calculation
  select("Growth")


resultsGrow <-
  #table of initial and final size data
  results %>% 
    select("Day", "Treatment", "Temperature", "pH", "TankID", "Diam1", "Diam2") %>% 
    drop_na(Diam1, Diam2) %>% 
    gather(key = "1or2", value = "Diameter", "Diam1", "Diam2") %>% 
    filter(Day == "126")
resultsGrow <- bind_cols(resultsGrow, Growth)
#combines table of initial and final with growth information

#Figure out means of each treatment group
resultsGrow %>% 
  dplyr::group_by(Temperature, pH) %>% 
  dplyr::summarise(mean = mean(Growth), s.e. = se(Growth)) %>% 

  kbl(caption = "Table 6: Growth means (%) +/- se after 126 days") %>% 
  kable_classic_2() %>% 
  kable_styling(c("striped", "hover"), full_width = F, html_font= "Times New Roman")

Table 6: Growth means (%) +/- se after 126 days

Temperature	pH	mean	s.e.
ambient	acidified	326.5950	16.290140
ambient	ambient	323.1710	10.963618
heated	acidified	352.0342	15.002253
heated	ambient	376.3414	7.147267

Growth ANOVA results

#LMM for growth:
modGrow <-
  resultsGrow %>% 
  aov(Growth~ Temperature * pH, data=.)

summary(modGrow)

##                Df Sum Sq Mean Sq F value  Pr(>F)   
## Temperature     1  16750   16750   8.257 0.00634 **
## pH              1   1096    1096   0.540 0.46642   
## Temperature:pH  1   2197    2197   1.083 0.30396   
## Residuals      42  85202    2029                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Check assumptions for growth model

## ASSSUMPTIONS
# 1. Normality of residuals
qqPlot(residuals(modGrow)) 

## [1] 38 34

shapiro.test(residuals(modGrow)) #passes

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(modGrow)
## W = 0.98242, p-value = 0.7064

hist(residuals(modGrow)) #looks normal

## ASSSUMPTIONS
# 2. Equal variances
leveneTest(residuals(modGrow)~resultsGrow$Treatment) #Passes

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value  Pr(>F)  
## group  3  2.3134 0.08975 .
##       42                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(fitted(modGrow),resid(modGrow,type="pearson"),col="blue")

Power analysis for test

pwr.anova.test(k=4, n= 5.75, f=0.7, sig.level = 0.05) #balanced one way anova

## 
##      Balanced one-way analysis of variance power calculation 
## 
##               k = 4
##               n = 5.75
##               f = 0.7
##       sig.level = 0.05
##           power = 0.7202639
## 
## NOTE: n is number in each group

#k=Number of groups - 4 treatments
#n=Number of observations (per group) - 5.75 to account for 1 dead
#f=Effect size - 0.5 based on some readings, but not sure if that's right
#sig.level=Significance level (Type I error probability)
#power=Power of test (1 minus Type II error probability)


pwr.f2.test(u=1, v=42, f=0.7, sig.level = 0.05) #general linear model

## 
##      Multiple regression power calculation 
## 
##               u = 1
##               v = 42
##              f2 = 0.7
##       sig.level = 0.05
##           power = 0.9997292

#u  = degrees of freedom for numerator
#v  = degrees of freedom for denominator
#f2 = effect size
#sig.level  = Significance level (Type I error probability)
#power  = Power of test (1 minus Type II error probability)

resultsGrowTime <-  #create table of growth in treatments
  results %>% 
  select("Day", "TankID", "Treatment","Temperature","pH","Growth") %>%
  drop_na(Growth) %>% 
  group_by(Day, Treatment) %>%
  mutate(se = (std.error(Growth))*100) %>%
  mutate(meanPct = (mean(Growth)*100))

modelGrowTime <- lmer(Growth~Temperature*pH + (1|TankID), data=resultsGrowTime)
summary(modelGrowTime) #generate results

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Growth ~ Temperature * pH + (1 | TankID)
##    Data: resultsGrowTime
## 
## REML criterion at convergence: 1181.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.66228 -0.87498  0.05818  0.82380  2.19934 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  TankID   (Intercept) 0.00     0.000   
##  Residual             1.27     1.127   
## Number of obs: 382, groups:  TankID, 24
## 
## Fixed effects:
##                              Estimate Std. Error        df t value
## (Intercept)                   1.77781    0.11504 378.00000  15.454
## Temperatureheated             0.09323    0.16269 378.00000   0.573
## pHambient                    -0.03635    0.16269 378.00000  -0.223
## Temperatureheated:pHambient   0.03893    0.23069 378.00000   0.169
##                             Pr(>|t|)    
## (Intercept)                   <2e-16 ***
## Temperatureheated              0.567    
## pHambient                      0.823    
## Temperatureheated:pHambient    0.866    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Tmprtr pHmbnt
## Tempertrhtd -0.707              
## pHambient   -0.707  0.500       
## Tmprtrhtd:H  0.499 -0.705 -0.705
## convergence code: 0
## boundary (singular) fit: see ?isSingular

anova(modelGrowTime, type=2)

## Type II Analysis of Variance Table with Satterthwaite's method
##                 Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Temperature    1.21056 1.21056     1   378  0.9529 0.3296
## pH             0.02757 0.02757     1   378  0.0217 0.8830
## Temperature:pH 0.03618 0.03618     1   378  0.0285 0.8661

i. Growth over time plot across all treatments

#### Growth Across Treatments
results %>% 
  select("Day", "Treatment","Temperature","pH","Growth") %>%
  drop_na(Growth) %>% 
  group_by(Day, Treatment) %>%
  mutate(se = (std.error(Growth))*100) %>%
  mutate(meanPct = (mean(Growth)*100)) %>% 

  
ggplot(aes(Day, meanPct, shape = Treatment, color = Treatment)) +
    geom_point(size = 2.5) +
    geom_line() +
    scale_x_continuous(name="Time (Day)", breaks = seq(0,130, by = 10)) +
    scale_y_continuous(name="Growth (%)", breaks = seq(0,400, by = 25)) +
    geom_errorbar(aes(ymin = meanPct-se, ymax = meanPct+se, width = 1.5)) +
    theme_classic() + 
    scale_shape_discrete(name = NULL,
                         labels = c("Amb T, Amb pH", "Amb T, Low pH", "High T, Amb pH", "High T, Low pH")) +
    scale_colour_manual(name = NULL,
                        values = c("gray40", "skyblue3", "firebrick3","mediumpurple3"),
                        labels = c("Amb T, Amb pH", "Amb T, Low pH", "High T, Amb pH", "High T, Low pH")) +
    theme(legend.margin = margin(0), 
          legend.position = c(.1, .98), 
          legend.justification = c("left", "top"),
          legend.background = element_blank())

ggsave(filename="Figures/20200611/GrowthTreatments.png", dpi=300, width=8, height=6, units="in")

ii. Growth over time plot by temperature

results %>% 
  select("Day","Temperature","Growth") %>%
  drop_na(Growth) %>% 
  group_by(Day, Temperature) %>%
  mutate(se = (std.error(Growth))*100) %>%
  mutate(meanPct = (mean(Growth)*100)) %>% 

  
  ggplot(aes(Day, meanPct, shape = Temperature, color = Temperature)) +
    geom_point(size = 2.5) +
    geom_line() +
    scale_x_continuous(name="Time (Day)", breaks = seq(0,130, by = 10)) +
    scale_y_continuous(name="Growth (%)", breaks = seq(0,400, by = 25)) +
    geom_errorbar(aes(ymin = meanPct-se, ymax = meanPct+se, width = 1.5)) +
    theme_classic() +
    scale_colour_manual(name = NULL, 
                        values = c("gray40", "firebrick3"), 
                        labels = c("Ambient Temperture", "High Temperature")) +
    scale_shape_discrete(name = NULL, 
                       labels = c("Ambient Temperture", "High Temperature")) +
    theme(legend.margin = margin(0), 
          legend.position = c(.03, .93), 
          legend.justification = c("left", "top")) + 
    annotate("text", x = 0, y = 375, label = "(a)") +
    annotate("text", x = 130, y = 359, label = "*", size = 7)

iii. Growth over time plot by pH

results %>% 
  select("Day","pH","Growth") %>%
  drop_na(Growth) %>% 
  group_by(Day, pH) %>%
  mutate(se = (std.error(Growth))*100) %>%
  mutate(meanPct = (mean(Growth)*100)) %>% 

  ggplot(aes(Day, meanPct, shape = pH, color = pH)) +
    geom_point(size = 2.5) +
    geom_line() +
    scale_x_continuous(name="Time (Day)", breaks = seq(0,130, by = 10)) +
    scale_y_continuous(name="Growth (%)", breaks = seq(0,400, by = 25)) +
    geom_errorbar(aes(ymin = meanPct-se, ymax = meanPct+se, width = 1.5)) +
    theme_classic() +
    scale_colour_manual(name = NULL, 
                        values = c("skyblue3", "gray40"), 
                        labels = c("Low pH", "Ambient pH")) +
    scale_shape_discrete(name = NULL,
                         labels = c("Low pH", "Ambient pH")) +
    theme(legend.margin = margin(0), 
          legend.position = c(.03, .93), 
          legend.justification = c("left", "top")) + 
    annotate("text", x = 0, y = 370, label = "(b)")

i. Calcification Ratio Analysis at the tips

Assemble data for chosen spine tips (distal end)

### Model 1: calcification at the tips of spines

resultsTip <- 
  #create data using only the SEM images of the tips of spines.
  results %>% 
  select ("Treatment", "Temperature", "pH", "PartOfSpine", "Chosen", "RatioSEM", "TankID") %>% 
    #selects for desired variables. PartOfSpine is tip or base, Chosen indicates which side of the image (arbitrary) is selected for (aka has no dust)
  drop_na(RatioSEM) %>% 
  filter(Chosen == "yes", PartOfSpine == "Tip")
    #filters only for tips and chosen side. No dusty images to be analyzed.

Results for spine tips with linear mixed model

#LMM for calcification at the tips of spines 
modTip <-
  resultsTip %>% 
  lmer(RatioSEM ~ Temperature * pH + (1|TankID), data = .)

summary(modTip)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RatioSEM ~ Temperature * pH + (1 | TankID)
##    Data: .
## 
## REML criterion at convergence: 64.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.76413 -0.74507 -0.02052  0.63045  2.07630 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  TankID   (Intercept) 0.0000   0.0000  
##  Residual             0.1356   0.3682  
## Number of obs: 67, groups:  TankID, 23
## 
## Fixed effects:
##                             Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                  1.69118    0.08930 63.00000  18.938   <2e-16
## Temperatureheated           -0.06662    0.12453 63.00000  -0.535   0.5945
## pHambient                   -0.07462    0.12453 63.00000  -0.599   0.5512
## Temperatureheated:pHambient  0.30557    0.18089 63.00000   1.689   0.0961
##                                
## (Intercept)                 ***
## Temperatureheated              
## pHambient                      
## Temperatureheated:pHambient .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Tmprtr pHmbnt
## Tempertrhtd -0.717              
## pHambient   -0.717  0.514       
## Tmprtrhtd:H  0.494 -0.688 -0.688
## convergence code: 0
## boundary (singular) fit: see ?isSingular

anova(modTip, type="II") #anova{stats}.Compute analysis of variance (or deviance) tables for one or more fitted model objects. Produces Type II Analysis of Variance Table with Satterthwaite's method.

## Type II Analysis of Variance Table with Satterthwaite's method
##                 Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
## Temperature    0.10158 0.10158     1    63  0.7492 0.39000  
## pH             0.08185 0.08185     1    63  0.6038 0.44006  
## Temperature:pH 0.38685 0.38685     1    63  2.8534 0.09612 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Check assumptions for calcification at tip model.

## ASSSUMPTIONS
# 1. Normality of residuals
qqPlot(residuals(modTip)) #Normal

## [1] 38  8

shapiro.test(residuals(modTip)) #Pass

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(modTip)
## W = 0.97737, p-value = 0.2605

hist(residuals(modTip))

# 2. Equal variances
leveneTest(residuals(modTip)~resultsTip$Treatment) #Pass

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.4545  0.715
##       63

plot(fitted(modTip),resid(modTip,type="pearson"),col="blue") 

ii. Calcification Ratio Analysis at the base

Assemble data for chosen spine bases (proximal end)

### Model 2: calcification in the base of the spines

resultsBase <-
   #create data using only the SEM images of the base of spines.
  results %>% 
  select ("Treatment", "Temperature", "pH", "PartOfSpine", "Chosen", "RatioSEM", "TankID") %>% 
    #selects for desired variables. PartOfSpine is tip or base, Chosen indicates which side of the image (arbitrary) is selected for (aka has no dust)
  drop_na(RatioSEM) %>% 
  filter(Chosen == "yes", PartOfSpine == "Base")
    #filters only for tips and chosen side. No dusty images to be analyzed.

Results for spine bases with linear mixed model

#LMM for calcification at the tips of spines 
modBase <- 
  resultsBase %>% 
  lmer(RatioSEM~ Temperature * pH + (1|TankID), data=.)

summary(modBase) 

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RatioSEM ~ Temperature * pH + (1 | TankID)
##    Data: .
## 
## REML criterion at convergence: 98.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5535 -0.6315 -0.1529  0.6918  1.9937 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  TankID   (Intercept) 0.1303   0.3610  
##  Residual             0.1597   0.3996  
## Number of obs: 68, groups:  TankID, 23
## 
## Fixed effects:
##                             Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)                   2.1440     0.1749 18.8077  12.257 2.06e-10
## Temperatureheated             0.3566     0.2487 19.1707   1.434   0.1677
## pHambient                     0.6524     0.2474 18.8077   2.637   0.0163
## Temperatureheated:pHambient  -0.2224     0.3594 18.9804  -0.619   0.5434
##                                
## (Intercept)                 ***
## Temperatureheated              
## pHambient                   *  
## Temperatureheated:pHambient    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Tmprtr pHmbnt
## Tempertrhtd -0.703              
## pHambient   -0.707  0.497       
## Tmprtrhtd:H  0.487 -0.692 -0.688

anova(modBase, type="II") #anova{stats}.Compute analysis of variance (or deviance) tables for one or more fitted model objects. Produces Type III Analysis of Variance Table with Satterthwaite's method.

## Type II Analysis of Variance Table with Satterthwaite's method
##                 Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Temperature    0.30743 0.30743     1 18.992  1.9251 0.181362   
## pH             1.48873 1.48873     1 18.960  9.3223 0.006553 **
## Temperature:pH 0.06114 0.06114     1 18.980  0.3829 0.543424   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Check assumptions for calcification at base model.

## ASSSUMPTIONS
# 1. Normality of residuals
qqPlot(residuals(modBase)) #Normal

## [1] 33 37

shapiro.test(residuals(modBase)) # Pass

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(modBase)
## W = 0.97304, p-value = 0.1472

hist(residuals(modBase))

# 2. Equal variances
leveneTest(residuals(modBase)~resultsBase$Treatment) #Pass

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3   1.068  0.369
##       64

plot(fitted(modBase),resid(modBase,type="pearson"),col="blue")

iii. Figure 4: Calcification Ratio Interaction Plot at tips and bases

Make Interaction plots for calcification at the base and the tip

#### Tip and base calcification ratios

#base
basesummary<-results %>% 
  select("Temperature","pH","RatioSEM", "PartOfSpine") %>%
  filter(PartOfSpine=="Base")%>%
  drop_na(RatioSEM) %>% 
  group_by(pH, Temperature, PartOfSpine) %>%
  summarize(mean = mean(RatioSEM), se = std.error(RatioSEM), N = length(RatioSEM))
  
baseplot<- ggplot(data=basesummary, aes(x=Temperature, y=mean, color = pH, group=interaction(Temperature,pH))) +
    geom_point(size = 3,  position=position_dodge(0.1)) +
    geom_line(aes(group=pH),  position=position_dodge(0.1)) +
    xlab("Temperature Treatment") +
    ylab("Proximal Calcification Ratio")+
    ylim(1,3.5)+
    geom_errorbar(aes(ymin = mean-se, ymax = mean+se, width = 0.1), position=position_dodge(0.1)) +
    theme_bw() + 
    scale_x_discrete(limits=c("ambient", "heated"), 
                     label=c("Ambient", "High"))+
    scale_colour_manual(name = "pH Treatment",
                        values = c("skyblue3", "gray40"),
                        labels = c("Acidified", "Ambient"),
                        guide = guide_legend(reverse = TRUE)) +
    geom_text(x=1.5, y=1.6, label="p(pH)=0.002", size=6, color="black") + 
    geom_text(x=1.5, y=1.4, label="p(Temperature)=0.16", size=6, color="darkgray") + 
    geom_text(x=1.5, y=1.2, label="p(Interaction)=0.54", size=6, color="darkgray") + 
    theme_classic()+
    theme(legend.position = "right", 
          legend.background = element_blank(), 
          axis.title = element_text(size = 16, face="bold"),
          axis.text = element_text(size = 14), 
          plot.title = element_text(size=16, face="bold"),
          legend.text = element_text(size=14), 
          legend.title = element_text(size=16, face="bold"));baseplot

#ggsave("CalcRatiobase.png", plot=baseplot, path = "/Users/emilysesno/Desktop/R_Analysis/R_Analysis/output",  width = 7, height = 5)  

ggsave(filename="Figures/20200611/BaseCalcificationFig.png", plot=baseplot, dpi=300, width=8, height=6, units="in")

#tip
tipsummary<-results %>% 
  select("Temperature","pH","RatioSEM", "PartOfSpine") %>%
  filter(PartOfSpine=="Tip")%>%
  drop_na(RatioSEM) %>% 
  group_by(pH, Temperature, PartOfSpine) %>%
  summarize(mean = mean(RatioSEM), se = std.error(RatioSEM), N = length(RatioSEM))

tipplot<-ggplot(data=tipsummary, aes(x=Temperature, y=mean, color = pH, group=interaction(Temperature,pH))) +
    geom_point(size = 3,  position=position_dodge(0.1)) +
    geom_line(aes(group=pH),  position=position_dodge(0.1)) +
    xlab("Temperature Treatment") +
    ylab("Distal Calcification Ratio")+
    ylim(1,3.5)+
    geom_errorbar(aes(ymin = mean-se, ymax = mean+se, width = 0.1), position=position_dodge(0.1)) +
    theme_bw() + 
    scale_x_discrete(limits=c("ambient", "heated"), 
                     label=c("Ambient", "High"))+
    scale_colour_manual(name = "pH Treatment",
                        values = c("skyblue3", "gray40"),
                        labels = c("Acidified", "Ambient"),
                        guide = guide_legend(reverse = TRUE)) +
    geom_text(x=1.5, y=3.0, label="p(pH)=0.44", size=6, color="darkgray") + 
    geom_text(x=1.5, y=2.8, label="p(Temperature)=0.39", size=6, color="darkgray") + 
    geom_text(x=1.5, y=2.6, label="p(Interaction)=0.09", size=6, color="darkgray") + 
    theme_classic()+
    theme(legend.position = "none", #removed the legend for the tip, so when we align them horizontally we only have one legend. But need to adjust the size so it is the same as base
          legend.background = element_blank(), 
          axis.title = element_text(size = 16, face="bold"),
          axis.text = element_text(size = 14), 
          plot.title = element_text(size=16, face="bold"),
          legend.text = element_text(size=14), 
          legend.title = element_text(size=16, face="bold"));tipplot

#ggsave(filename="Figures/20200611/TipCalcificationFig.png", plot=tipplot, dpi=300, width=8, height=6, units="in")

Combine both interaction plots at base and tip to be in horizontal line

i. Spine Loss Analysis:

Assemble data for dropped spines

## Number of loose spines counted at the bottom of tanks at the end of the experiment. These were either broken or shed. Note: these spines were not collected, just counted, so can not determine whether they were broken or shed.

resultsDropped <-
  #create data using only the needed variables.
  results %>% 
  select ("Treatment", "Temperature", "pH", "SpineCount", "TankID") %>% 
  drop_na(SpineCount) %>% 
  group_by(pH) %>% 
  mutate(mean = mean(SpineCount),
         se = std.error(SpineCount))

Analyse dropped spines with linear mixed effect model.

##LM of dropped spines - can't make it LMM because error: number of levels of each grouping factor must be < number of observations - only have one count for each TankID.
modDropped <- 
  resultsDropped %>% 
  lm(SpineCount~ Temperature * pH, data=.)

summary(modDropped)

## 
## Call:
## lm(formula = SpineCount ~ Temperature * pH, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.0000  -6.0833  -0.1667   0.4000  20.0000 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   21.167      3.640   5.814 1.33e-05 ***
## Temperatureheated             -1.167      5.148  -0.227  0.82315    
## pHambient                    -21.000      5.148  -4.079  0.00064 ***
## Temperatureheated:pHambient    1.600      7.461   0.214  0.83248    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.917 on 19 degrees of freedom
## Multiple R-squared:  0.6088, Adjusted R-squared:  0.547 
## F-statistic: 9.855 on 3 and 19 DF,  p-value: 0.0003899

anova(modDropped) #anova{stats}.Compute analysis of variance (or deviance) tables for one or more fitted model objects. Produces Type III Analysis of Variance Table with Satterthwaite's method.

## Analysis of Variance Table
## 
## Response: SpineCount
##                Df  Sum Sq Mean Sq F value    Pr(>F)    
## Temperature     1    1.52    1.52  0.0192    0.8914    
## pH              1 2345.78 2345.78 29.4995 3.062e-05 ***
## Temperature:pH  1    3.66    3.66  0.0460    0.8325    
## Residuals      19 1510.87   79.52                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Check assumptions for model for dropped spines

##ASSUMPTIONS
# 1. Normality of residuals
qqPlot(residuals(modDropped)) #not normal

## [1] 2 4

shapiro.test(residuals(modDropped)) #faaaiiilll

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(modDropped)
## W = 0.86706, p-value = 0.005636

hist(residuals(modDropped))

# 2. Equal variances
leveneTest(residuals(modDropped)~resultsDropped$Treatment) # barely pass

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value  Pr(>F)  
## group  3  2.8487 0.06483 .
##       19                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(fitted(modDropped),resid(modDropped,type="pearson"),col="blue")

Analysis for dropped spines does not meet assumptions. Attempt a square root transformation.

##DOES NOT MEET ASSUMPTIONS so ATTEMPT AT Transformation:
resultsDropped$tdata<-(resultsDropped$SpineCount)^1/2
  # transformation
modDropped1 <- lm(tdata~ Temperature * pH, data=resultsDropped)
  # run lm model of transformed data

###ASSUMPTIONS for Transformation
# 1. Normality of residuals
qqPlot(residuals(modDropped1)) #not normal

## [1] 2 4

shapiro.test(residuals(modDropped1)) #fail

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(modDropped1)
## W = 0.86706, p-value = 0.005636

hist(residuals(modDropped1))

# 2. equal variances
bartlett.test(residuals(modDropped1)~resultsDropped$Treatment) #fail

## 
##  Bartlett test of homogeneity of variances
## 
## data:  residuals(modDropped1) by resultsDropped$Treatment
## Bartlett's K-squared = 43.282, df = 3, p-value = 2.144e-09

plot(fitted(modDropped1),resid(modDropped1,type="pearson"),col="blue")

summary(modDropped1)

## 
## Call:
## lm(formula = tdata ~ Temperature * pH, data = resultsDropped)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0000 -3.0417 -0.0833  0.2000 10.0000 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  10.5833     1.8202   5.814 1.33e-05 ***
## Temperatureheated            -0.5833     2.5742  -0.227  0.82315    
## pHambient                   -10.5000     2.5742  -4.079  0.00064 ***
## Temperatureheated:pHambient   0.8000     3.7304   0.214  0.83248    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.459 on 19 degrees of freedom
## Multiple R-squared:  0.6088, Adjusted R-squared:  0.547 
## F-statistic: 9.855 on 3 and 19 DF,  p-value: 0.0003899

Anova(modDropped1, type=2) #test for significance of model

## Anova Table (Type II tests)
## 
## Response: tdata
##                Sum Sq Df F value    Pr(>F)    
## Temperature      0.23  1  0.0118    0.9146    
## pH             586.44  1 29.4995 3.062e-05 ***
## Temperature:pH   0.91  1  0.0460    0.8325    
## Residuals      377.72 19                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Transfomraiton (of any usual kind) of dropped spines was not successful, so we use a non parametric Kruskal Wallis Test.

### Transformations not work, so use non parametric:
kruskal.test(resultsDropped$SpineCount~resultsDropped$Treatment)# SIG*** (p=0.0005563)

kruskal.test(resultsDropped$SpineCount~resultsDropped$Temperature)# 
kruskal.test(resultsDropped$SpineCount~resultsDropped$pH)#

Conduct Dunn Post Hoc Test for dropped spines

## POST HOC Pairwise
dunn <- 
  resultsDropped %>% 
  dunnTest(SpineCount ~ Treatment,
           method = "holm", kw = TRUE, data = .)
dunnph <- dunn$res
cldList(P.adj ~ Comparison, data = dunnph, threshold = 0.05)

##   Group Letter MonoLetter
## 1   AMB      a        a  
## 2    OA      b         b 
## 3     T     ac        a c
## 4  T/OA     bc         bc

ii. Figure 5: Spine Loss Interaction Plot

droppedsummary<-results %>% 
  select("Temperature","pH","SpineCount") %>%
  drop_na(SpineCount) %>% 
  group_by(pH, Temperature) %>%
  summarize(mean = mean(SpineCount), se = std.error(SpineCount), N = length(SpineCount))

  dropplot<-ggplot(data=droppedsummary, aes(x=Temperature, y=mean, color = pH, group=interaction(Temperature,pH))) +
    geom_point(size = 3,  position=position_dodge(0.1)) +
    geom_line(aes(group=pH),  position=position_dodge(0.1)) +
    xlab("Temperature Treatment") +
    ylab("Dropped Spines")+
    geom_errorbar(aes(ymin = mean-se, ymax = mean+se, width = 0.1), position=position_dodge(0.1)) +
    ylim(0,30) +
    theme_bw() + 
    scale_x_discrete(limits=c("ambient", "heated"), 
                     label=c("Ambient", "High"))+
    scale_colour_manual(name = "pH Treatment",
                        values = c("skyblue3", "gray40"),
                        labels = c("Acidified", "Ambient"),
                        guide = guide_legend(reverse = TRUE)) +
    #geom_text(x=1.5, y=11, label="p(pH)<0.001", size=6, color="black") + 
    #geom_text(x=1.5, y=9, label="p(Temperature)=0.91", size=6, color="darkgray") + 
    #geom_text(x=1.5, y=7, label="p(Interaction)=0.83", size=6, color="darkgray") +
    theme_classic()+
    theme(legend.position = "right", 
          legend.background = element_blank(), 
          axis.title = element_text(size = 16, face="bold"),
          axis.text = element_text(size = 14), 
          plot.title = element_text(size=16, face="bold"),
          legend.text = element_text(size=14), 
          legend.title = element_text(size=16, face="bold"));dropplot

#ggsave(filename="Figures/20200611/DroppedSpinesFig.png", plot=dropplot, dpi=300, width=8, height=6, units="in")